Question

if the distance between the point A(2,-2) and B(-1,X) is equal to 5 then the value of X is?​

Answer 1

Answer:

If the distance between the point A(2,-2) and B(-1,X) is equal to 5

If x is 2 :-B = (-1 , x) = (-1 , 2)

If x is - 6 :-B = (-1 , x) = (-1 , -6)

Step-by-step explanation:

A (2,-2) = (x_1,y_1)

B(-1,x) = (x_2,y_2)

Distance   $=\sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}$

d(AB)

$=\sqrt{(-1-2)^2 + (X- (-2))^2} = 5\\\sqrt{(-3)^2 + (x +2)^2} = 5\\\sqrt{9 + x^2 + 4x + 4 }= 5 \\\sqrt{ x^2 + 4x + 13 }= 5 \\x^2 + 4x + 13 = 25$

x² + 4x + 13 - 25 = 0

x² + 4x - 12 = 0

x² + 6x - 2x - 12 = 0

x(x + 6) - 2(x + 6) = 0

(x - 2) (x + 6) = 0

x = 2 , - 6

∴ Value of 'x' can be 2 , - 6.

If x is 2 :-B = (-1 , x) = (-1 , 2)

If x is - 6 :-B = (-1 , x) = (-1 , -6)